C₅×#23700 #11946420

order	1280
nilpotency class	3
isoclinism	isoclinic class of #1999
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₅ · Schur multiplier (H₂) = C₂⁴

Aliases

	subgroup	G/H
center	C₂²×C₄×C₅	C₂×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₅
socle	C₂³×C₅	C₂²×D₄
prime radical	C₂×C₅×#121	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₅ ◁ C₂²×C₄²×C₅ ◁ G

978 conjugacy classes of subgroups.

minimal degree	μ(G) = 25
transitive degree	μ_t(G) = 640

A minimal faithful permutation representation — 4 generators on 25 points:

(1,2,3,4,5)(10,11)(12,15)(13,14)(16,17)(18,19,22,23,21,25,20,24);(6,7)(8,9)(11,14)(15,17);(7,9)(19,23)(20,22)(24,25);(10,12,13,16)(11,15,14,17)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1280, 16688);